Method for operating a linear compressor
A method for operating a linear compressor is provided. The method includes estimating an acceleration of the motor of the linear compressor using at least a robust integral of the sign of the error feedback. A position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point is also determined based at least in part on a measured current to the motor of the linear compressor and an estimated acceleration of the motor. The position of the motor of the linear compressor when the motor of the linear compressor is at a top dead center point is calculated based at least in part on the position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point and a stroke length of the motor of the linear compressor.
1. A method for operating a linear compressor, comprising:
providing a mechanical dynamic model for the linear compressor, the mechanical dynamic model for the linear compressor comprises
x
¨
=
-
C
M
x
.
-
K
M
(
x
avg
-
x
0
)
+
α
M
i
+
1
M
F
gas
=
α
M
i
+
f
x
(
t
)
where
f
x
(
t
)
=
1
M
F
gas
-
C
M
x
.
-
K
M
(
x
avg
-
x
0
)
+
α
M
i
M is a moving mass of the linear compressor,
α is a motor force constant of a motor of the linear compressor,
i is a current through the motor of the linear compressor,
{umlaut over (x)} is an acceleration of the motor of the linear compressor,
C is a damping coefficient of the linear compressor,
{dot over (x)} is a velocity of the motor of the linear compressor,
K is a spring stiffness of the linear compressor,
x is a position of the moving mass of the linear compressor,
x avg is an average position of the moving mass of the linear compressor, and
F gas is a gas force;
supplying the motor of the linear compressor with a time varying voltage;
measuring a current to the motor of the linear compressor during said step of supplying, a velocity of the motor of the linear compressor being zero when the motor of the linear compressor is at a bottom dead center point during said step of measuring;
calculating an observed acceleration of the motor of the linear compressor using at least the mechanical dynamic model for the linear compressor and a robust integral of the sign of the error feedback by solving
x
¨
^
=
α
M
i
+
f
^
x
(
t
)
with {circumflex over (f)} x being given as
f
^
x
=
(
k
1
+
1
)
e
x
(
t
)
+
∫
t
0
t
[
(
k
1
+
1
)
e
x
(
σ
)
+
k
2
sgn
(
e
x
(
σ
)
)
]
d
σ
-
(
k
1
+
1
)
e
x
(
t
0
)
and where
{umlaut over ({circumflex over (x)})} is the observed acceleration of the motor of the linear compressor,
k 1 and k 2 are real, positive gains,
sgn is the signum function,
e x is an error given as {dot over (x)}−{dot over ({circumflex over (x)})},
{dot over ({circumflex over (x)})} is an observed velocity of the motor of the linear compressor,
e x (σ) is e x as a function of σ,
e x (t) is e x as a function of time, and
e x (t 0 ) is e x at time t 0 ;
determining a position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point based at least in part on the current to the motor of the linear compressor at the bottom dead center point from said step of measuring and the observed acceleration of the motor;
calculating the position of the motor of the linear compressor when the motor of the linear compressor is at a top dead center point based at least in part on the position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point from said step of determining and a stroke length of the motor of the linear compressor; and
adjusting the time varying voltage supplied to the motor of the linear compressor in response to the calculated position of the motor of the linear compressor.
2. The method of claim 1 , wherein the linear compressor is positioned within a refrigerator appliance.
3. The method of claim 1 , said step of determining the position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point comprises solving
x
BDC
=
α
K
i
BDC
-
M
K
x
¨
BDC
where
i BDC is the current to the motor of the linear compressor from said step of measuring; and
{umlaut over (x)} BDC is the observed acceleration of the motor.
4. The method of claim 3 , wherein said step of calculating the position of the motor of the linear compressor when the motor of the linear compressor is at a top dead center point comprises solving
x TDC =x BDC −SL
where SL is the stroke length of the motor of the linear compressor.
5. The method of claim 1 , wherein said steps of estimating, determining and calculating are conducted with the motor of the linear compressor sealed within a hermetic shell of the linear compressor.
6. A method for operating a linear compressor, comprising:
supplying a motor of the linear compressor with a time varying voltage, the motor of the linear compressor disposed within a hermetic shell of the linear compressor during said step of supplying;
measuring a current to the motor of the linear compressor during said step of supplying, a velocity of the motor of the linear compressor being zero when the motor of the linear compressor is at a bottom dead center point during said step of measuring;
calculating an observed acceleration of the motor of the linear compressor using a robust integral of the sign of the error feedback by solving
x
¨
^
=
α
M
i
+
f
^
x
(
t
)
with {circumflex over (f)} x being given as
f
^
x
=
(
k
1
+
1
)
e
x
(
t
)
+
∫
t
0
t
[
(
k
1
+
1
)
e
x
(
σ
)
+
k
2
sgn
(
e
x
(
σ
)
)
]
d
σ
-
(
k
1
+
1
)
e
x
(
t
0
)
and where
{umlaut over ({circumflex over (x)})} is the observed acceleration of the motor of the linear compressor,
k 1 and k 2 are real, positive gains,
sgn is the signum function,
e x is an error given as {dot over (x)}−{dot over ({circumflex over (x)})},
{dot over ({circumflex over (x)})} is an observed velocity of the motor of the linear compressor,
e x (σ) is e x as a function of σ,
e x (t) is e x as a function of time, and
e x (t 0 ) is e x at time t 0 ;
determining a position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point based at least in part on the current to the motor of the linear compressor from said step of measuring and the observed acceleration of the motor by solving
x
BDC
=
α
K
i
BDC
-
M
K
x
¨
BDC
where
α is a motor force constant of the motor of the linear compressor,
K is a spring stiffness of the linear compressor,
i BDC is the current to the motor of the linear compressor from said step of measuring,
M is a moving mass of the linear compressor, and
{umlaut over (x)} BDC is the observed acceleration of the motor;
calculating the position of the motor of the linear compressor when the motor of the linear compressor is at a top dead center point based at least in part on the position of the motor of the linear compressor when the motor of the linear compressor is at the bottom dead center point from said step of determining and a stroke length of the motor of the linear compressor; and
adjusting the time varying voltage supplied to the motor of the linear compressor in response to the calculated position of the motor of the linear compressor.
7. The method of claim 6 , wherein the linear compressor is positioned within a refrigerator appliance.
8. The method of claim 6 , wherein said step of calculating the position of the motor of the linear compressor when the motor of the linear compressor is at a top dead center point comprises solving
x TDC =x BDC −SL
where SL is the stroke length of the motor of the linear compressor.